Your baby's head movement development will get stronger by the time he is 1 to 2 months old. Till then, you need to support his head and neck as you hold him. Having proper head control is a very crucial milestone of his development as it will help in further progress of your child. It will aid in other things like sitting, walking, standing, watching, having solid foods, etc.
Initially, it is little difficult for your baby to move his head. He may even get frustrated while turning his head. Encourage him to lie on his tummy while he is awake. Keep colourful toys around him or call him. Make sure your baby's head movements are side to side as he lifts his chin off the floor, and turns to see you or the toy, his neck muscles will get strong. Around 6 months you will see him having better head control. Your baby's head movements while sleeping will progress slowly, do not rush with it.
Disclaimer : Content presented here is for information purposes only, please consult with your doctor for any health queries